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A047887
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Triangle of numbers T(n,k) = number of permutations of n things with longest increasing subsequence of length <=k (1<=k<=n).
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5
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1, 1, 2, 1, 5, 6, 1, 14, 23, 24, 1, 42, 103, 119, 120, 1, 132, 513, 694, 719, 720, 1, 429, 2761, 4582, 5003, 5039, 5040, 1, 1430, 15767, 33324, 39429, 40270, 40319, 40320, 1, 4862, 94359, 261808, 344837, 361302, 362815, 362879, 362880, 1, 16796
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OFFSET
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1,3
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LINKS
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EXAMPLE
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Triangle T(n,k) begins:
1;
1, 2;
1, 5, 6;
1, 14, 23, 24;
1, 42, 103, 119, 120;
1, 132, 513, 694, 719, 720;
1, 429, 2761, 4582, 5003, 5039, 5040;
...
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MATHEMATICA
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h[l_] := Module[{n = Length[l]}, Total[l]!/Product[Product[1 + l[[i]] - j + Sum[If[l[[k]] >= j, 1, 0], {k, i + 1, n}], {j, 1, l[[i]]}], {i, 1, n}]];
g[n_, i_, l_] := If[n == 0 || i == 1, h[Join[l, Array[1 &, n]]]^2, If[i < 1, 0, Sum[g[n - i*j, i - 1, Join[l, Array[i &, j]]], {j, 0, n/i}]]];
T[n_] := Table[g[n - k, Min[n - k, k], {k}], {k, 1, n}] // Accumulate;
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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